Apparatus and method for real time and real flow-rate measurement of multi-phase fluids

ABSTRACT

A method for measuring flow rate of at least one fluid in a multi-phase fluid comprises: providing a magnetic resonance module through which the fluid phases flow and at least one pre-polarization module of variable effective length upstream of the magnetic resonance module; and conducting, a measurement by: i) setting the pre-polarization module to have a first effective length, ii) applying a RF pulse sequence to the fluid, in the magnetic resonance module, iii) determining the intensity of a pre-determined number of spin echoes produced by the RF pulse sequence, iv) determining a line approximating the attenuation of the intensity during the RF sequence, v) determining slope and y-intercept of the line, vi) determining the ratio of the slope and intercept, vii) applying a calibration between the slope:intercept ratio and multi-phase flow rate so as to determine the flow velocity of the fluid in the multi-phase fluid.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a divisional of Ser. No. 12/749,308, filedMar. 29, 2010, which claims priority of U.S. application Ser. No.11/608,042, filed 7 Dec. 2006, which claims priority to ArgentineanPatent Application No P06 01 00100 filed 11 Jan. 2006, all of which areincorporated by reference.

FIELD OF INVENTION

This invention relates to a method and apparatus for real time and realproduction volumes measurements of flow-rates and proportions of acomplex fluid consisting of a multiple-component heterogeneous blend.Particularly, this invention applies to the separate measurement offlow-rates and relative proportions (or cuts) of oil and water in oil,water and gas heterogeneous blends, both at the production line (orvein) from oil wells and other ducts which distribute various types offluids. Proposed method and instrument allow measurement of flow ratesof the individual components of the complex fluid in a non-invasive,non-destructive way, and regardless of the blend condition, i.e., forexample, a blend consisting of separate phases of oil, water and gas o asingle emulsion phase. This invention solves the problem of previoussolutions, which are limited to total maximum flow-rates amounting to afew tens of cubic meters of fluid per day.

BACKGROUND

Components at the production line are very seldom found in pure state,as they rather form emulsions or heterogeneous blends which relativeproportions change with time Said condition is typically termed“multiphase”. This particularity of the fluid to be measured preventsuse of conventional flow-meters, which may only measure total fluidflow-rate, as they are unable of identifying proportions of eachparticular component. Measurement errors are generally importantbecause, among other factors, passage of gas in non-homogeneousproportions instantaneously modifies rheological properties of themultiple phase. The most used method actually consists of deviatingproduction towards a temporal storage tank, collecting said generallydaily production and, once components have separated by the action ofgravity, relative volumes are measured. This method poses multipleimplementing problems, as:

a) due to several reasons, it is not possible to completely separateblend components, such reasons may include:

1. formation of a water-oil emulsion interface, which may amount to asignificant volume in the storage tank; and

2. natural settlement always results in a certain quantity of waterremaining in emulsion with oil

b) even where both components could be adequately separated, devicesused for interface measuring are difficult to implement, as, forexample, it is not possible to establish water or oil levels by simplelevel inspection.

c) in fact, this technique only allows control of the individualproduction of each well on, a monthly frequency at most.

As regards the real time application of measurement techniques in theoil production, special consideration should be given to the fact thatgas tends to flow at higher speeds than liquid components. Thus, gasflow-rate measurements should be necessarily performed separately fromliquid components, or else such flow Velocity should be measured onceall of the components of the blend are adequately mixed.

Other more sophisticated techniques have been invented which are basedon different measuring principles. As an example we can mention thesimple Venturi tube, the Coriolis principle, ultrasound, gamma raysmeasuring, and Magnetic Resonance (NMR).

The first technique is based on the measurement of the pressuredifference existing between both ends of a tube with variable section.Measurements performed by means of this method strongly depend from thegas which is dispersed or bubbles within the blend. Further, this methoddoes not discriminate the multiphase composition.

Coriolis's mass flow-meter is a mechanical design in which flow passagethrough a curved duct or other medium produces the vibration ofmechanical parts thereof. Two or more vibration sensors are installed onthe device, said sensors being positioned at a certain distance one fromeach other in the flow direction. Such flow produces vibrations atpre-established resonance frequencies which depend on the material andshape of said mechanical parts, but vary according to mass flow density(for more details see U.S. Pat. No. 4,187,721). It is also possible toderivate a phase difference between the resonance frequencies of bothsensors, which angle, divided by the resonance frequency f, isproportional to the flow mass proportion (for more details see U.S. Pat.No. 5,648,616 or EP-A-866 319). As this method involves mechanicalinteractions, it is also strongly dependent on the fluidcompressibility, which in turn strongly depends on the gas proportion,both that gas which is dissolved within the vein and that which bubblesthrough it.

Another design which does not exhibit moving mechanical parts is basedon the ultrasound emission and reception in order to measure transittime of the fluid through the carrying vein. The time taken by theultrasound wave in arriving to the receptor element since its emissionand through the liquid flow, is proportional to the fluid speed withinthe carrying conduct. The fluid blend is obviously used as the couplingsubstance between the emitting crystal and the receptor. Here again, gasplays an essential role as regards the evaluation of measurement errors.On the one hand, bubbles break said coupling and introduce veryimportant errors both as regards the propagation time of the acousticsignal and the attenuation of the sound wave. Even where bubbles areabsent, compressibility of the liquid medium strongly depends from thequantity of gas dissolved therein, this being a variable, whichremarkably affects measurement process and result.

However, the Nuclear Magnetic Resonance principle allows bothmeasurements to be done: i) determination of oil, gas and waterproportions in the fluid blend, and ii) determination of the flow speedof said blend. There exist several patents which disclose methods—notnecessarily selective as regards multiphase fluids—which use NMRanalysis. Among them., the following can be mentioned: 1) Rollwitz etal., Method and Apparatus for Coal Analysis and Flow Measurements, U.S.Pat. No. 4,531,093; 2) King et al. Method and Apparatus for MeasuringFlow in a Pipe of Conduit, U.S. Pat. No. 4,536,711, and 3) Reichwein,Consistency Measuring Device, U.S. Pat. No. 4,866,385.

Previous art devices designed for flow measuring and/or flow mapping arebased on two widely known principles: 1) “time of flight” of saturatedor unsaturated spins on the NMR spectrometer magnetic field; 2) on whatis known as spatial codification of spins phase as they displace on amagnetic field gradient.

State of the art is completed with those patents which disclose specificmethods for measuring flow-rate of multiphase fluids:

U.S. Pat. No. 4,785,245, entitled Rapid Pulse NMR Cut Meter describes aflow-meter which employs an NMR analysis in order to determine thefraction of one of the components of a multi-phase fluid flowing througha production line. NMR signal amplitude of a certain component isobtained by means of a pulse sequence which radio-frequency is adequatefor the relative relaxation times between fluid components. This Patentdoes not disclose a simultaneous method able to measure flow-rate of oneof the phases which signal has separated. That is to say, it requiresanother device in order to measure flow velocity of said component.

U.S. Pat. No. 6,046,587, Measurements of Flow Fractions, Flow Velocitiesand Flow Rates of a Multiphase Fluid using NMR Sensing and U.S. Pat. No.6,268,727, Measurements of Flow Fractions, Flow Velocities and FlowRates of a Multiphase Fluid using ESR Sensing, both to J. D. King, Q. Niand A. de los Santos, disclose a sensor which employs at least two NMRspectrometers or one NMR spectrometer and another ESR (ElectronicParamagnetic Resonance) one. Basic principle of measurement methodologyis based on what is known as “time of flight” between bothspectrometers. Such system of two spectrometers which separately measureresidence time of each phase at the magnetic field is of unpractical andcostly implementation: also, its application is difficult in the case ofoil fields, which are generally subject to harsh climates. Anothervariant of said patents are those filed with the INPI (ArgentineIndustrial Property Institute) No. 010104816 (Oct. 12, 2001) and patentpending in USA 2004/0015332, by M. Ramia, D. J. Pusiol, C. A. Martin, E.Fried and R. Garnero. This case comprises a single electronic part whichis shared by two sensing coils, operation principle being that alreadydescribed, that is, flow velocity is measured through time of flight ofwater and oil molecules through the space between both sensing coils.This device exhibits the same restrictions as that involving twospectrometers: measurable flow-rate is substantially lower than 100m³/day for the total fluid.

Flow-meter with phase separation disclosed by U.S. Pat. No. 6,452,390,by E. Wollin, entitled Magnetic Resonance Analyzing Flow Meter and FlowMeasuring Method, proposes a methodology and associated apparatus whichimplementation is simpler than those already described. This methodologyuses pulsed magnetic fields gradients in order to modulate the spins (orprotons) precession phase. That is to say that spatial codification iscarried out by which is commonly known as Laboratory System. The problemwith this method is that at the common displacement velocities ofprotons on the magnetic field, magnetic field gradients application istechnologically difficult to apply, due to the fact that, in order toproduce an adequate magnetic field gradient, it is necessary to includeimportant currents which on/off times are generally relatively long.That is to say that this methodology is generally restricted torelatively small flow-rates measurements.

Another variant of said patents are those tiled with the INPI under No.P040102415 on Jul. 8, 2004, and the pending US patent publication no2006/0020403, by SpinLock SRL and D. J. Pusiol. Said applicationsdisclose a flow-meter and cut sensor comprising a single coil associatedto slanted planar plates magnet which generates a constant magneticfield, along with a magnetic field gradient. Said application furtherdiscloses the application of a pre-polarization field for rapid fluids,which may be removed in the case of slow fluids. Said application alsodiscloses a derivation device with electronic key which allowsmeasurement of N sensors groups with a single electronic system. In saidapplication, spatial codification of the resonant nuclei position iscarried out through a linear gradient of the magnetic field at the placeof the excitation/Magnetic Resonance detection coil, which is preferablygenerated by the slanted position of the polar faces of a permanentmagnet. In the case of high flow velocities, said gradient must beincreased in order to attain the necessary effectiveness of the spatialcodification process of the NMR spectrum of those protons forming themoving complex fluid. Upon the increase of said magnetic field gradientthe Magnetic Resonance signal broadens and thus deteriorates. Themaximum flow-rate limit measurable by means of this invention is givenby the maximum value of magnetic field gradient that may be applied tothe fluid passing through the sensor tube before the signaldeteriorates, preventing the precision required for the particular use.

The inventive flow-meter employs a measurement method which is based onthe passing time of the fluid molecules at a single sensor, withoutusing any magnetic field gradient for fluid velocity measurements. Thismethod consists of the ultrafast irradiation of hydrogen nucleibelonging to said molecules through repeated pulses within short timeintervals, following a CPMG type sequence (see, e.g. A. Abragham, ThePrinciples or Nuclear Magnetism, Oxford University Press, 19981; thus,the temporal evolution of the NMR signal depends from the number of“refreshment” molecules appearing in the volume of theexcitation/detection coil. In turn, for a given interval betweenexcitation pulses, said number of refreshment molecules depends on thefluid velocity at the production line. This invention is based on thefact that there exists a region of the CPMG sequence, in which the spinechoes amplitude following application of each radio-frequency pulseexhibits a linear variation with time Quotient between the slope of saidlinear relation and origin ordinate is proportional to flow velocity,whereas the origin ordinate contains information which allows thedetermination of the proportion of the different elements comprising thecomplex fluid, which produce a detectable NMR signal.

In order to establish the relative proportions within the heterogeneousblend of the production fluid (we are preferably referring to oil, waterand gas proportions), the production duct is first introduced through aspins pre-polarization magnetic module and then through a magneticresonance sensor module. Length of said pre-polarization field and thevelocity of the complex fluid establish a passage time of said flowwhich, along with the relaxation time T₁ of the spins species which formpart of one of the components of the complex fluid, allows protonspresent in the complex fluid portion to attain a polarization sufficientto produce a magnetic resonance signal in the magnetic resonance sensormodule. Polarization of a particular component on the pre-polarizationfield is selected by adjusting length thereof in such a way that itsprotons will attain enough polarization so as to provide a NMR signal.In order to select the Magnetic Resonance signal of the componentexhibiting a longer relaxation time, there is added to thepre-polarization magnetic field a second field (temporarily pulsed),extending its action on the production vein. That is to say that, inthis situation, ordinate at the origin of adjustment of the linearregion of the echoes of the CPMG sequence, after a repeated pulsessequence, will now represent protons from two of the fluid components,each with higher and lower T₁. From the quantitative comparison ofordinates at the origin of both signals, one which is obtained with ashorter length of the pre-polarization field and the other obtained withlonger spatial length for the application of the pre-polarization field,relative proportions, or cuts, of both components are obtained. Wherethe fluid bears a third component, an adequately arranged third magneticfield will be added.

Measurements are sequentially carried out and appropriately repeated inorder to obtain an adequate signal-to-noise relation. Typically,measurement is completed in a few seconds.

Accordingly, this invention may be applied in all those cases involvingcomplex fluids circulation, as for instance: Oil-Water, Mud from MiningOperations, Industrial Fluids, etc.

SUMMARY

Accordingly, it is an object of the present application an apparatus andmethod for measuring flow-rate and cut of oil production in real timeand volumes, which comprises, mutually associated, a magnetic resonancesensor module, a pulsed pre-polarization magnetic module of variablelength, a radio-frequency electronic module for magnetic resonance, amagnetic resonance digital module and a control computer.

Still another object of the present invention is a method for the directmeasurement in real time and flow-rates of the proportion and flow-rateof the different components which form a multiple-component complexfluid, which method makes use of the above device, said methodcomprising the following steps:

-   a. activation of the first segment of the pre-polarization magnetic    field in order to pre-polarize resonant nuclei of said    multiple-component complex fluid during a time adequate regarding    the spin-lattice, relaxation time T₁ of said first selected    component in order to establish proportion and flow-rate thereof;-   b. transmission of radio-frequency pulses through a transmitter    T_(x) included in said radio-frequency electronic module, according    to the CPMG pulses sequence;-   c. emission of said radio-frequency pulses from said radio-frequency    electronic module towards said magnetic resonance sensor module in    order to excite, said resonant nuclei of said complex fluid and    generate a magnetic resonance signal (NMR) as a response to said    emitted radio-frequency pulses;-   d. reception of response signals at said sensor assembly;-   e. emission of said signals in said sensor assembly through said    receiver R_(x), included in said radio-frequency electronic module;-   f. digitalization of said response signals received by an    analog/digital converter which is included in said magnetic    resonance digital module;-   g. transference of said digitalized signals to said control    computer; and-   h. activation of said second segment of said pre-polarization    magnetic field in order to pre-polarize said resonant nuclei of said    multiple-component complex fluid during a time appropriate as    regards the value of said second shorter spin-lattice relaxation    time T₁ of said selected second component for the determination of    its proportion and flow-rate;-   i. repetition of steps b) to h) in order to obtain adequate signals    for their further mathematical analysis in order to obtain relative    proportions and flow-rates of the different components of said    complex fluid;-   j. activation of said third segment of said pre-polarization    magnetic field in order to pre-polarize said resonant nuclei of said    multiple-component complex fluid during a time appropriate as    regards the value of said third shorter spin-lattice relaxation time    T₁ of said selected third component for the determination of its    proportion and flow-rate;-   k. repetition of steps b) to j) in order to obtain adequate signals    for their further mathematical analysis in order to obtain relative    proportions and flow-rates of the different components of said    complex fluid;-   l. repetition of said steps until all the measurable components are    measured; m. by means of adequate mathematical operations,    processing of the obtained resonance signals in order to obtain    proportion and flow-rate of each of the components of the complex    fluid.

Still another object of the present invention is a sensor assembly,comprising said magnetic resonance sensor module and said pulsedpre-polarization magnetic, module of variable length.

Still another object is an arrangement of production lines formultiple-components complex fluids which uses the above device, whereineach of the various production lines of multiple-components complexfluids bears one of said sensor assemblies fixedly mounted; or a singlesensor assembly is fixedly mounted on an auxiliary production linetowards which the different complex fluid production lines converge.

Still another object is to prevent sensitivity to flow-rate measurementfrom showing peculiar interference effects, by means of theneutralization of eventual shifts at the NMR frequency, due to changesof the B0 value on account of environmental thermal effects.

Still another object of the present invention is measuring of velocitiesprofiles within the volume of the complex fluid distribution pipe.

Still another object is that said sensors are fixed or movable.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention shall be better understood when referring to the followingfigures:

FIG. 1 illustrates a simplified block diagram of the preferred assemblyaccording to the present invention.

FIG. 2 illustrates the experimental behavior of the polarization factorf(v) in function of flow velocity v for two oil components (T₁=160 msand T=640 ms) and formation water (T₁1.44 s).

FIG. 3 illustrates behavior of polarization factor f(v) at thevelocities v range comprised from 0.1 and 1.5 m/s for two oil components(T₁=160 ms and T₁=640 ms) and formation water (T₁=1.44 s).

FIG. 4 shows the succession of echoes obtained upon the application ofthe CPMG sequence, for oil circulating at a velocity of 1.1 m/s.

FIG. 5 illustrates amplitudes of the Fourier Transforms of CPMGsequences echoes for oil circulating at different velocities.

FIG. 6 shows dependence quotient 13/A, between slope (B) and originordinate (A) of linear adjustments of CPMG sequences, in function of theexperimentally established mean velocity of fluid.

FIG. 7 illustrates experimental behavior of origin ordinates of linearadjustments of CPMG sequences for fluids comprised of differentconcentrations of oil and water circulating at a mean velocity of 1.1m/s in function of oil concentration x_(p).

FIG. 8 illustrates experimental behavior of origin ordinates of linearadjustments of CPMG sequences for fluids comprised of differentconcentrations of oil and water circulating at a mean velocity of 1.1m/s in function of oil concentration x_(p), for two different lengths ofthe pre-polarization stage, L₁-0.5 m and L₂=0.9 m.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 illustrates a simplified block diagram of the preferred assemblyaccording to the present invention, Complex fluid circulates throughproduction vein 1 and passes through a magnetic field generated at thepre-polarization Magnetic Module 2. Then, complex fluid passes throughthe Magnetic Resonance Sensor Module 3 through which the fluid isexcited and its corresponding response signal is detected. ControlComputer 4 is used for the synchronization of the complex fluidmeasurement process. Magnetic Resonance Electronic Module 5 is used, onthe one hand, in order to generate RF pulses used for exciting thecomplex fluid and on the other hand for the demodulation of theresonance signal from the fluid after the excitation. Digital module 6is used both for synthesizing pulses which modulate the RF produced atthe Radio-Frequency Electronic Module 5 and for the digitalization ofthe signal demodulated at the Magnetic Resonance Radio-FrequencyElectronic Module 5. Length along which magnetic field is applied on thePre-Polarization Magnetic Module is Variable and may be adjusted by theDriver module 7.

Measurement of fluid mean velocity and phases proportion: the preferredmethod for measuring mean velocity of total fluid as well as theproportion of phases present in a multiphase fluid consists of theutilization of a pulses sequence known by the previous art as CPMG, withat least two phases producing a detectable NMR signal. Said sequenceCPMG is a pulses sequence π/2—π- . . . -π, so that magnetization whichwill be rotating on plan x-y (detection plan) will be constructed withthose portions of the sample originally excited by the first pulse ofthe sequence (pulse of π/2) and which induce an electromotive force atthe detection coil. Temporal origin of sequence (t=0) is defined as theinstant in which the π/2 pulse application begins. During such shortinterval all of the fluid volume inside the detection coil is excited.

In order to better understand the invention, without loss of generality,analysis is restricted to the simplest case in which the fluid consistsof two phases, for example one of them being formation water and theother oil: and further, wherein the production tube is completely fullof fluid during the measuring process.

Thus, in t=0 total volume of fluid will be:

V _(T)(0)=V _(A)(0)V _(I)(0)   (1)

wherein V_(A) y V_(E) are, respectively, the volume occupied by each ofthe two phases present in the fluid.

Where the fluid displaces at a mean velocity V₁, sample volume producinga detectable signal at time t will be:

V _(T)(t)=V _(T)(0)−S vt   (2)

wherein S is the cross-section of the detection (solenoidal) coil.

At time t the following equations should also be satisfied:

V _(A)(t)=(0)−S _(A) vt=S _(A l () L−vt)   (3)

V _(B)(t)=V _(B)(0)−S _(B) vt=S _(B)(L−vt)   (4)

S _(A) +S _(B) =S   (5)

wherein S_(A) and S_(B) represent effective cross-sections correspondingto phases A and B respectively and L represents the length of detectioncoil.

By dividing equation (3) by equation (4) we have:

$\begin{matrix}{\frac{V_{A}(t)}{V_{B}(t)} = \frac{S_{A}}{S_{B}}} & (6)\end{matrix}$

Previous equation evaluated at time t=0 and time t implies:

$\begin{matrix}{\frac{V_{A}(t)}{V_{B}(t)} = \frac{V_{A}(0)}{V_{B}(0)}} & (7)\end{matrix}$

This means that in this approximation, at any time within the durationinterval of the CPMG sequence, the relative volume proportions of bothphases are equal to those existing at t=0 when the pulses sequencebegan. Thus, equations (3), (4) y (7) are easily deduced from thefollowing expressions:

$\begin{matrix}{{V_{A}(t)} = {{V_{A}(0)}\left( {1 - {\frac{v}{L}t}} \right)}} & (8) \\{{V_{B}(t)} = {{V_{B}(0)}\left( {1 - {\frac{v}{L}t}} \right)}} & (9)\end{matrix}$

On the other hand, intensity of signal CPMG at time t=nτ (wherein τ isthe separation between two consecutive π pulses of the CPMG sequence),shall be given by the following expression:

$\begin{matrix}{{I\left( {v,t} \right)} = {{{I_{A}\left( {v,t} \right)}^{- \frac{t}{T_{2{eff}}^{A}}}} + {{I_{B}\left( {v,t} \right)}^{- \frac{t}{T_{2{eff}}^{B}}}}}} & (10)\end{matrix}$

wherein:

$\begin{matrix}{{I_{\alpha}\left( {v,t} \right)} = {{{M_{\alpha}(v)}{V_{\alpha}(t)}} = {{M_{\alpha}(v)}{V_{\alpha}(0)}\left( {1 - {\frac{v}{L_{eff}}t}} \right)}}} & (11)\end{matrix}$

In equation (11) M_(a)(v) represents magnetization by volume unit ofcomponent a circulating at a mean velocity v, V_(a) (0) is the volume ofcomponent a at the beginning of sequence CPMG (t=0), T _(2ef) ^(a) isthe effective spin-spin time of relaxation of component a, v is the meanvelocity of flow, and L_(eff) represents the effective length ofexcitation coil.

By means of equation (11), equation 10 may be expressed as

$\begin{matrix}{{I\left( {v,t} \right)} = {\left\lbrack {{{M_{A}(v)}{V_{A}(0)}^{- \frac{t}{T_{2{eff}}^{A}}}} + {{M_{B}(v)}{V_{B}(0)}^{- \frac{t}{T_{2{eff}}^{B}}}}} \right\rbrack \left( {1 - {\frac{v}{L_{eff}}t}} \right)}} & (12)\end{matrix}$

Naturally, the expression (12) only has sense in those time I instantssatisfying 0≦1−(v/L)t≦1.

Correction by pre-polarization factor: As the fluid is moving, in orderto obtain a net magnetization which may be observed at the detectioncoil it is necessary to polarize it before it enters theexcitation/detection coil. Typically this is achieved by placing anassembly of magnets along length L_(pol) on the path immediatelypreceding the permanent magnet of the Magnetic Resonance module.Considering that the fluid moves at velocity v, the magnetization netfraction along direction z, perpendicular to flow direction, shall begiven by the following equation:

$\begin{matrix}{{f_{\alpha}\left( {v,L_{pol}} \right)} = {\frac{M_{\alpha}(v)}{M_{\alpha}(0)} = \left( {1 - ^{- \frac{L_{pol}}{{vT}_{1}^{\alpha}}}} \right)}} & (13)\end{matrix}$

Coefficient f_(a)(v) is named pre-polarization factor. FIG. 2 shows thetypical behavior of f_(a)i(v) in function of the velocity of the fluidfor formation water (T₁=1.4 s) and two oil types (T₁−160 ms and T₁=640ms) for polarization lengths L₁=0.5m and L₂=0.9m. FIG. 3 shows anenlargement of FIG. 2 at velocities from 0.1 to 1.5 m/s.

As can be seen in FIG. 3, the signal intensity at the end of thepre-polarization stage undergoes significant changes when using apre-polarization stage of 50 cm or 90 cm long. These changes are morenoticeable in the case of those fluid components which relaxation timesdo not satisfy L_(pol)/(vT₁)<<1.

Taking into account, the pre-polarization factor f_(e)(v), theexpression (12) is finally transformed into:

$\begin{matrix}{{I\left( {v,t} \right)} = {\left\lbrack {{{f_{A}(v)}M_{0}^{A}{V_{A}(0)}^{- \frac{t}{T_{2{eff}}^{A}}}} + {{f_{B}(v)}M_{0}^{B}{V_{B}(0)}^{- \frac{t}{T_{2{eff}}^{B}}}}} \right\rbrack \left( {1 - {\frac{v}{L_{eff}}t}} \right)}} & (14)\end{matrix}$

wherein M₀ ^(a) denotes M_(a)(0). Equation (14) and behavior ofpre-polarization factors f_(a)(v), suggest two possible methods forapproaching the problem of the simultaneous determination of the meanvelocity of fluid and phase fractions present in a fluid of two phases.

Determination of fluid mean velocity: An important remark as regardsequation (14) is that, in the case of values satisfying simultaneouslyconditions t/T^(A) _(2eff)<<1 and t/T^(B) _(2eff)<<1, said expression isreduced to:

$\begin{matrix}{{I\left( {v,t} \right)} = {\left\lbrack {{{f_{A}(v)}M_{0}^{A}{V_{A}(0)}} + {{f_{B}(v)}M_{0}^{B}{V_{B}(0)}}} \right\rbrack \left( {1 - {\frac{v}{L_{eff}}t}} \right)}} & (15)\end{matrix}$

Expression (15) denotes that if we perform an adjustment of theamplitude of the echoes corresponding to the lineal region of the CPMGsequence, through an expression in the form of I(v,t)=A+Bt, quotient B/Abetween slope and origin ordinate of adjustment is directly proportionalto the mean velocity of fluid, proportionality constant being equal tothe reciprocal of the effective length of the excitation/detection coil(antenna).

Determination of components Fraction with fixed length pre-polarizationstage (Method D. Expression 15 shows that for a given mean velocity v offluid, the origin ordinate of adjustment of the region in which the CPMGsignal intensity varies linearly, determines the sum of intensities dueto the volume of each present phase, weighted with the polarizationfactors f_(a)(v) of each phase.

In some cases it is possible that the lineal approximation be invalidand thence adjustment of experimental data by means of expression (14)could be problematic due to the presence of two exponential functions.However, in such eases it is possible to use expression (14) bearing inmind that if separation τ between consecutive pulses of π is much lowerthan T^(A) _(2eff) and T^(B) _(2eff) then:

I(v,τ)≈I(v, 0)≡I ₀(v)=[f _(A)(v)M ₀ ^(A) V _(A)(0)+f _(B)(v)M ₀ ^(B) V_(B)(0)]=A(v)+B(v)   (16)

wherein I(v, τ) is the height of the first echo of the CPMG sequence.Thus, it is possible to adjust the following expression to theexperimental data:

$\begin{matrix}{{I\left( {v,t} \right)} = {\left\lbrack {{{A(v)}^{- \frac{t}{T_{2{eff}}^{A}}}} + {\left( {{I\left( {v,\tau} \right)} - {A(v)}} \right)^{- \frac{t}{T_{2{eff}}^{B}}}} +} \right\rbrack \left( {1 - {\frac{v}{L_{eff}}t}} \right)}} & (17)\end{matrix}$

Generally, exponentials present in equation (17) may be approached bythe first terms of their. Taylor development, which remarkablyfacilitates adjustment of expression (17) to experimental data.

In those cases in which the circulating fluid comprises two phases, e.g.oil and water, the origin ordinate of adjustment of the CPMG sequencethrough expressions (15) or (17) will be given by the followingexpression:

I ₀(v)=x _(p) I _(p) ⁰(v)+(1−x _(p))I _(w) ⁰(v)   (18)

wherein:

x_(p): oil fraction

I_(p) ⁰(v): origin ordinate for total oil content moving at velocity v

I_(w) ⁰(v) : origin ordinate for total water content moving at velocityv

$\begin{matrix}{{{I_{0}(v)} = {\underset{\underset{C{(v)}}{}}{x_{p}\left( {{I_{p}^{0}(v)} - {I_{w}^{0}(v)}} \right)} + \underset{\underset{D{(v)}}{}}{I_{w}^{0}(v)}}}{{I(v)} = {{x_{p}{C(v)}} + {D(v)}}}} & (19)\end{matrix}$

From expression (19) it can be clearly seen that for a given meanvelocity v and that of the fluid, there exists a linear relation betweenthe lineal adjustment origin ordinate and the oil fraction x_(p) presentin the fluid. Thence, if we perform an adjustment of the origin ordinatevalues for different known oil x_(p) concentrations by means ofexpression (19) we may obtain coefficients C(v) and D(v). Once C(v) andD(v) are known, it is possible to obtain value of an unknown oil x_(p)concentration through the expression:

x _(p)=(I(v)−D(v))/C(v)   (20)

Determination of components Fraction with variable lengthpre-polarization stage (Method 2). We will define coefficient γ₁(v) asthe quotient of the pre-polarization factors of stage a circulating atmean velocity v, for two different lengths L₁ and L₂ of thepre-polarization stage:

$\begin{matrix}{{\gamma_{\alpha}(v)} = {\frac{f_{\alpha}\left( {v,L_{2}} \right)}{f_{\alpha}\left( {v,L_{1}} \right)} = \frac{\left( {1 - ^{- \frac{L_{2}}{{vT}_{1}^{\alpha}}}} \right)}{\left( {1 - ^{- \frac{L_{1}}{{vT}_{1}^{\alpha}}}} \right)}}} & (21)\end{matrix}$

Alternatively using a pre-polarization stage of length L₁ and thenanother one of length L₂ we will see that, essentially, origin ordinatesof the adjustments of each of the pulses sequences satisfy the followingequations:

I ₀₁(v)=I _(p1)(v)+I _(w1)(v)   (22)

I ₀₂(v)=I _(p2)(v)+I _(w2)(v)   (23)

Also, the following relations are satisfied:

$\begin{matrix}\left\{ \begin{matrix}{{\frac{I_{p\; 2}}{I_{p\; 1}} = {\gamma_{p}(v)}}} \\{\frac{I_{w\; 2}}{I_{w\; 1}} = {{\gamma_{w}(v)}(25)}}\end{matrix} \right. & (24)\end{matrix}$

Using rotations (24) and (25) and equations (22) and (23), we easilyfind that values of unknown quantities I_(p1) and I_(w1) correspond to:

$\begin{matrix}{{I_{p\; 1}(v)} = \frac{{{\gamma_{w}(v)}{I_{01}(v)}} - {I_{02}(v)}}{\left( {{\gamma_{w}(v)} - {\gamma_{p}(v)}} \right)}} & (26) \\{{I_{w\; 1}(v)} = \frac{{{\gamma_{p}(v)}{I_{01}(v)}} - {I_{02}(v)}}{\left( {{\gamma_{p}(v)} - {\gamma_{w}(v)}} \right)}} & (27)\end{matrix}$

Once calibration values of I⁰ _(p)(v) and I⁰ _(w)(v) are known when eachof the phases is separately moving at a mean velocity v within a fullduct, we are able to calculate absolute flow-rates of oil and formationwater circulating through the pipe in the presence and absence of gas,air or a mixture thereof.

FIG. 4 illustrates a typical CPMG sequence for pure oil circulating at avelocity of 1.1 m/s. Insert of said figure shows the region of the CPMGsequence which was enlarged at the bottom of FIG. 4. It may be clearlyappreciated that echoes amplitude varies in a linear fashion at thebeginning of the CPMG sequence, where (t/T_(2eff)<<I) is satisfied.

FIG. 5 shows amplitudes of FFT of CPMG sequences echoes performed forvarious flow velocities. It is clearly observed that FFT amplitudesfollow a linear behavior. Also, slope of these lines clearly responds tothe fluid, total velocity.

FIG. 6 shows dependency of the B/A quotient between slope (B) and theorigin ordinate (A) from linear adjustments of CPMG sequences infunction of the fluid velocity, this velocity having been experimentallyestablished. It can be clearly observed a linear dependency between bothmagnitudes.

Determination of oil and water content of a two-phases blend. Method 1.Fixed pre-polarization stage: FIG. 7 shows a graphic of the behavior oforigin ordinates of linear adjustments of CPMG sequences in function ofthe oil x_(p) concentration, by means of expression (15). Two zones areclearly observed. One for concentrations x_(p) lower than 0.5, namedzone 1, and another for concentrations higher than said value, namedzone 2. It was experimentally established that pulse widths of π/2 (t)for each zone are different, namely 9 μs for zone 1 and 20 μs for zone2.

Determination of the zone corresponding to the fluid which componentsfraction is to be measured may be easily done by means of de comparisonof relative amplitudes of the first echo of two CPMG sequences, one witha pulse width of t_(w)=9 and the other with a pulse width of t_(w)=20 □s

From the linear adjustment of each zone there can be obtainedcoefficients C_(i) and D_(i) (i=1,2) which characterize the relationbetween A and x_(p).

A(v)=C _(i)(v)x _(p) +D _(i)(v)   (28)

After plotting a calibration curve as that shown by FIG. 7, fordifferent total flow velocities, v, coefficients C_(i) and D_(i) areknown and the oil fraction present in the fluid (and accordingly alsothat of water) is obtained though the following expression:

x _(p)=(A(v)−D(v))/C _(i)(v)   (29)

Method 2: variable pre-polarization stage: This method consists of theacquisition of two

CPMG sequences with different lengths of the pre-polarization stage.There follows an adjustment of each of the sequences through expressions(14), (15) or (17) as the case may be and the origin ordinates I₀₁(v)and I₀₂(v) are obtained, which correspond to pre-polarization lengths L₁and L₂, respectively. FIG. 8 shows typical behavior of origin ordinates(I₀(v)) of the adjustments of sequences CPMG through expression (15),for two different lengths of the pre-polarization stage (L₁=0.5 m(circles) and L₂=0.9 m (triangles)), in function of the concentration ofoil x_(p) for a fluid comprising oil and formation water. For a givenoil x_(p) concentration two different intensity values are observed,wherein the highest value corresponds to the highest pre-polarizationlength used.

On the other hand, we obtain effective coefficients γ₁ ^(eff)(v) fromthe experimental behavior of the coefficient of origin ordinates I₀₂^(a)(v)/I₀₁ ^(a)(v), for each of the NMR detectable phases circulatingseparately, with full pipe, in function of mean velocity v. In suchconditions, the following equations are satisfied:

$\begin{matrix}{{I_{01}(v)} = {{I_{p\; 1}(v)} + {I_{w\; 1}(v)}}} & (30) \\{{I_{02}(v)} = {{I_{p\; 2}(v)} + {I_{w\; 2}(v)}}} & (31) \\\left\{ \begin{matrix}{{\frac{I_{p\; 2}}{I_{p\; 1}} = {\gamma_{p}^{eff}(v)}}} \\{\frac{I_{w\; 2}}{I_{w\; 1}} = {{\gamma_{w}^{eff}(v)}(33)}}\end{matrix} \right. & (32)\end{matrix}$

By using relations (30) and (31) and equations (32) and (33) we caneasily find that unknown values of I_(p1)and I_(w1) correspond to:

$\begin{matrix}{{I_{p\; 1}(v)} = \frac{{{\gamma_{w}^{eff}(v)}{I_{01}(v)}} - {I_{02}(v)}}{\left( {{\gamma_{w}^{eff}(v)} - {\gamma_{p}^{eff}(v)}} \right)}} & (26) \\{{I_{w\; 1}(v)} = \frac{{{\gamma_{p}^{eff}(v)}{I_{01}(v)}} - {I_{02}(v)}}{\left( {{\gamma_{p}^{eff}(v)} - {\gamma_{w}^{eff}(v)}} \right)}} & (27)\end{matrix}$

Knowing calibration values I⁰ _(p)(v) and I⁰ _(w)(v) when each of thephases is separately circulating at a mean velocity v through a fullpipe, we may calculate absolute flow-rates of the two phases movingthrough such pipe, both in the presence of gas, air or a mixturethereof, or otherwise.

The above description refers to the measurement of mean velocity at theproduction duct. In order to establish the flow regime at the productionline, it is necessary to measure the velocity profile of the fluidcomponents on the plane perpendicular to flow direction. To such end,the NMR signal of each component of the fluid is selectively excited. Asusual, selective excitation is performed through a magnetic fieldgradient along said plane which is transversal to flow and theexcitation of the respective NMR signals through frequency-selectivepulses. The magnetic field gradient, shall be essentially confined tothe volume occupied by the radio-frequency coil of the magneticresonance sensor module and may be linear or radial to such plane.Selective radio-frequency pulses at the excitation frequency areamplitude—and/or phase-modulated, preferably through a “sync” function.Once the CPMG sequence with excitation spatial selection is applied,velocity of the fluid component, excited to a certain resonancefrequency, is obtained.

A preferred arrangement refers to the determination of the velocitiesprofile in a cylindrical section tube. The magnetic field at theMagnetic Resonance sensor module should bear a radial field gradient atthe plane transversal to flow direction. Selective excitation willprovide, for each CPMG measurement, mean velocity at a transversal ringwhich diameter will depend on the, magnetic field value and the resonantexcitation frequency. This procedure is repeated for different values,of the excitation frequency. Any person with average skill in the artmay design and implement a device to be added to the flow-meter in orderto perform the determination of the velocities profile directly in theproduction tube.

Whenever it says that an apparatus of this invention comprises,includes, contains, bears, is composed or consists of certaincomponents, it should be understood, unless otherwise stated, that oneor more components of those explicitly described may be present in theapparatus. In an alternative arrangement, however, the inventiveapparatus may be described as essentially consisting of said components,wherein components of said arrangement which may materially alter theoperation principle or distinctive features of the apparatus might notbe included in the description of said alternative arrangement. Inanother alternative arrangement, the inventive apparatus may bedescribed as consisting of certain components while other components ofsaid arrangement might not be described.

1. A method for measuring the flow velocity of at least one fluid ofinterest in a multi-phase fluid flowing in a pipe at a known overallflow rate, said fluid comprising first, second, and third fluid phases,the method comprising the steps of: a) providing an MRI-compatibledevice comprising: a magnetic resonance module through which the fluidphases flow; and at least one pre-polarization module producing apre-polarization magnetic field of variable effective length throughwhich the multi-phase fluid flows before entering the magnetic resonancemodule; wherein a previously determined velocity calibration of themagnetic resonance module, between slope : intercept ratios and flowvelocities for each of a plurality of fluids flowing through the device,is known and wherein each calibration is obtained by determining theslope : intercept ratio at each of a plurality of flow velocities;conducting a measurement comprising the steps of: i) setting thepre-polarization module so as to pre-polarize resonant nuclei of saidmulti-phase fluid for a time period that is adequate with respect to thespin-lattice relaxation time T_(i) of a first selected fluid phase; ii)applying in the magnetic resonance module a CPMG pulse sequencecorresponding to said first selected fluid phase so as to excite saidresonant nuclei and thereby generate a magnetic resonance signal; iii)determining the intensity of a pre-determined number of spin echoes thatare produced by the CPMG pulse sequence; iv) determining a line thatapproximates the attenuation of the intensity of the pre-determinednumber of spin echoes with increasing time during which the RF sequenceis applied; v) determining slope and y-intercept of the line determinedin step iv); vi) determining the ratio of the slope and the interceptdetermined in step v); vii) using the previously determined velocitycalibration in order to determine the flow velocity of the fluid ofinterest in the multi-phase fluid; and viii) providing the flow velocitydetermined in step b)vii) to a user; and
 2. The method according toclaim 2, further including using the determined flow velocity todetermine the fluid fraction of the first fluid in the multi-phase fluidby using a predetermined intensity calibration, for a module throughwhich only the first fluid is flowing, between signal intensity andfluid velocity at each of a plurality of velocities and comparing thedetected intensity to the single-fluid intensity at the determined, flowvelocity.
 3. The method according to claim 2, further includingrepeating step b) using a second setting of the pre-polarization moduleso as to determine the flow velocity of a second fluid of interest inthe multi-phase fluid and using, the determined flow velocity of thesecond fluid to determine the fluid fraction of the second fluid in themulti-phase fluid by using a predetermined calibration, for a modulethrough which only the second fluid is flowing, between signal intensityand fluid velocity at each of a plurality of velocities and comparingthe detected intensity to the single-fluid intensity at the determinedflow velocity for the second fluid.
 4. The method according to claim 3wherein said first and second fluids are oil and water.
 5. The methodaccording to claim 3 wherein the multi-phase fluid comprises water, oil,and gas.